Finite Group Databasebeta

← #14657483

Subgroups — #14657483

Order 2816.

406 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068608C211yesmaximal, characteristic
2#13067374C211yesmaximal, characteristic, complemented
3#13067306C211yesmaximal, characteristic, complemented
4#13067071C211yesmaximal, characteristic, complemented
5C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic
6#13066490C211yesmaximal, characteristic, complemented
7C11×#3077C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C11×#478—22no—
11C11×#476—21no—
12C11×#474—21no—
13C11×#428—21no—
14C11×#423C2211yescharacteristic
15C11×#418—21no—
16C2×#66897—21no—
17#10622537C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21#10622185—21no—
22#10622184—21no—
23Q8⋊(C11⋊C8)—21no—
24Q8⋊(C11⋊C8)—21no—
25D4⋊(C11⋊C8)—21no—
26D4⋊(C11⋊C8)—21no—
27#10622168—21no—
28#10622117—22no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C2×C11×M16—21no—
32C11×C4⋊Q8D411yescharacteristic
33C11×C4⋊Q8D411yescharacteristic
34C11×#125—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C11×#117—21no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×#4318—21no—
48C2×#4318—21no—
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51C11×#107—22no—
52C11×#106—22no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8D412yes—
55C11×#102—22no—
56C11×#102—22no—
57#66897—42no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4×C11⋊C8—21no—
65C4×C11⋊C8D411yescharacteristic
66C4×C11⋊C8D411yescharacteristic
67#10461—111nomaximal, Sylow
68C24×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11Q1612yes—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—81no—
81C22×C4×C11—81no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C11×M16—41no—
86C11×M16—41no—
87C2×C8×C11—22no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C42×C11—41no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11#4111yescharacteristic
104#4318—41no—
105#4318—41no—
106#4318—41no—
107#4318—41no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—42no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—81no—
115#3077D1111yescharacteristic
116#1800—111no—
117#1567—111no—
118#1550—111no—
119#1493—111no—
120C2×D4⋊C8—111no—
121#1292—111no—
122C23×C11—22no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—81no—
126C23×C11—81no—
127C23×C11#12311yescharacteristic
128Q8×C11—41no—
129Q8×C11—41no—
130Q8×C11—81no—
131D4×C11—22no—
132D4×C11—22no—
133D4×C11—41no—
134D4×C11—41no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—82no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C2×C4×C11#12411yescharacteristic
151C2×C4×C11C2×Q1611yescharacteristic
152C2×C4×C11#13511yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C11#13711yescharacteristic
155C8×C11—42no—
156C11⋊C8—22no—
157C11⋊C8—41no—
158C11⋊C8—81no—
159C11⋊C8—81no—
160C11⋊C8—81no—
161#533C2×D1111yescharacteristic
162C2×C4×D4C2×D1111yescharacteristic
163#478—22no—
164#476—21no—
165#474—21no—
166#428—21no—
167#423—111no—
168#423—111no—
169#423C2×D1111yescharacteristic
170C2×C4⋊C8—111no—
171#418—21no—
172C2×#100—221no—
173C2×C4×C8—111no—
174#343—221no—
175#335—222no—
176#333—221no—
177#332—221no—
178Q8⋊C8—221no—
179Q8⋊C8—221no—
180D4⋊C8—221no—
181D4⋊C8—221no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—42no—
185C22×C11—82no—
186C22×C11—82no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11#39411yescharacteristic
190C22×C11#48411yescharacteristic
191C22×C11#48511yescharacteristic
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11#44911yescharacteristic
199C4×C11#45111yescharacteristic
200C4×C11#46711yescharacteristic
201C4×C11#46811yescharacteristic
202C4×C11#47111yescharacteristic
203C4×C11#47211yescharacteristic
204C22×D4C22⋊D1111yescharacteristic
205C23×C4—21no—
206C2×M16—21no—
207C2×M16—221no—
208C2×M16—221no—
209C22×C8—221no—
210C22×C8—221no—
211C4⋊Q8C22⋊D1111yescharacteristic
212C4⋊Q8C22⋊D1111yescharacteristic
213#125—21no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×D4—21no—
219C4×D4—21no—
220C4×D4—21no—
221C4×D4—21no—
222#117—21no—
223C2×C4⋊C4C22⋊D1111yescharacteristic
224C2×C22⋊C4—21no—
225C2×C42C22×D1111yescharacteristic
226#107—22no—
227#106—22no—
228C4⋊C8—21no—
229C4⋊C8—221no—
230C4⋊C8—221no—
231C4⋊C8—221no—
232C4⋊C8—221no—
233C4⋊C8—221no—
234C4⋊C8—221no—
235C4⋊C8C22⋊D1112yes—
236#102—22no—
237#102—22no—
238#100—442no—
239C4×C8—111no—
240C4×C8—111no—
241C4×C8—221no—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11—82no—
245C2×C11#203611yescharacteristic
246C2×C11#205011yescharacteristic
247C2×C11#205111yescharacteristic
248C24—21no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4#432612yes—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4#434111yescharacteristic
263C22×C4#434111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265M16—41no—
266M16—41no—
267M16—441no—
268M16—441no—
269M16—441no—
270M16—441no—
271C2×C8—22no—
272C2×C8—221no—
273C2×C8—221no—
274C2×C8—442no—
275C2×C8—441no—
276C2×C8—441no—
277C2×C8—441no—
278C2×C8—881no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C42—41no—
291C42D4×D1111yescharacteristic
292C42#434111yescharacteristic
293C42C2×C22⋊D1111yescharacteristic
294C42C2×C22⋊D1111yescharacteristic
295C11#1046111yescharacteristic, complemented, Sylow
296C23—22no—
297C23—41no—
298C23—41no—
299C23—81no—
300C23—81no—
301C23#6698811yescharacteristic
302Q8—41no—
303Q8—41no—
304Q8—81no—
305D4—22no—
306D4—22no—
307D4—41no—
308D4—41no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—82no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4#6698811yescharacteristic
320C2×C4#6698911yescharacteristic
321C2×C4#6699111yescharacteristic
322C2×C4#6699211yescharacteristic
323C2×C4#6699211yescharacteristic
324C2×C4#6699511yescharacteristic
325C2×C4C2×#432611yescharacteristic
326C2×C4#6700211yescharacteristic
327C2×C4#6700311yescharacteristic
328C2×C4#6700611yescharacteristic
329C8—42no—
330C8—222no—
331C8—441no—
332C8—881no—
333C8—881no—
334C8—881no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—82no—
339C22—82no—
340C22—81no—
341C22—81no—
342C22#1062265711yescharacteristic
343C22#1062265811yescharacteristic
344C22#1062283511yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4#1062266211yescharacteristic
352C4#1062266411yescharacteristic
353C4#1062281211yescharacteristic
354C4#1062281311yescharacteristic
355C4#1062284111yescharacteristic
356C4#1062285111yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2#1306981611yescharacteristic
361C2#1306990011yescharacteristic
362C2#1306990511yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3077C2
socleC22×C11#394
prime radicalC22×D4×C11D4
hypercenter#3077D11
hypocenterC11#10461
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13067374C2semidirect
3. #13067306C2semidirect
4. #13067071C2semidirect
6. #13066490C2semidirect
295. C11#10461semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130686082
#130673742
#130673062
#130670712
C2×D4⋊(C11⋊C8)2
#130664902
C11×#30772
#1046111